UNPKG

mathmlben

Version:

Visualization for goldstandard

123 lines 13 kB
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="left-parenthesis n plus lamda right-parenthesis Superscript 1 minus lamda Baseline left-parenthesis 1 minus x squared right-parenthesis Superscript one-half lamda Baseline StartAbsoluteValue upper C Subscript n Superscript left-parenthesis lamda right-parenthesis Baseline left-parenthesis x right-parenthesis EndAbsoluteValue less-than StartFraction 2 Superscript 1 minus lamda Baseline Over normal upper Gamma left-parenthesis lamda right-parenthesis EndFraction"> <semantics> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-id="63" data-semantic-children="62,52" data-semantic-content="38"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="62" data-semantic-children="9,23,59" data-semantic-content="60,61" data-semantic-parent="63"> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="9" data-semantic-children="54,8" data-semantic-parent="62" data-semantic-fencepointer="4"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="54" data-semantic-children="53" data-semantic-content="0,4" data-semantic-parent="9"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="54">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="53" data-semantic-children="1,3" data-semantic-content="2" data-semantic-parent="54"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="53">n</mi> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="2" data-semantic-parent="53" data-semantic-operator="infixop,+">+</mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="3" data-semantic-parent="53">λ <!-- λ --> </mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="4" data-semantic-parent="54">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="8" data-semantic-children="5,7" data-semantic-content="6" data-semantic-parent="9"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="5" data-semantic-parent="8">1</mn> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="6" data-semantic-parent="8" data-semantic-operator="infixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="7" data-semantic-parent="8">λ <!-- λ --> </mi> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="60" data-semantic-parent="62" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="23" data-semantic-children="56,22" data-semantic-parent="62" data-semantic-fencepointer="16"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="56" data-semantic-children="55" data-semantic-content="10,16" data-semantic-parent="23"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="10" data-semantic-parent="56">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="55" data-semantic-children="11,15" data-semantic-content="12" data-semantic-parent="56"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="11" data-semantic-parent="55">1</mn> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="12" data-semantic-parent="55" data-semantic-operator="infixop,−"><!-- − --> </mo> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="15" data-semantic-children="13,14" data-semantic-parent="55"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="15">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="14" data-semantic-parent="15">2</mn> </mrow> </msup> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="16" data-semantic-parent="56">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="22" data-semantic-children="19,20" data-semantic-content="21" data-semantic-parent="23"> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="19" data-semantic-children="17,18" data-semantic-parent="22"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="17" data-semantic-parent="19">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="18" data-semantic-parent="19">2</mn> </mfrac> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="21" data-semantic-parent="22" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="20" data-semantic-parent="22">λ <!-- λ --> </mi> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="61" data-semantic-parent="62" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="neutral" data-semantic-id="59" data-semantic-children="58" data-semantic-content="24,37" data-semantic-parent="62"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="24" data-semantic-parent="59" data-semantic-operator="fenced">|</mo> </mrow> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="58" data-semantic-children="32,36" data-semantic-content="57,25" data-semantic-parent="59"> <msubsup data-semantic-type="subsup" data-semantic-role="simple function" data-semantic-id="32" data-semantic-children="25,26,30" data-semantic-parent="58" data-semantic-collapsed="(32 (31 25 26) 30)"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="25" data-semantic-parent="32" data-semantic-operator="appl">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="26" data-semantic-parent="32">n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="30" data-semantic-children="28" data-semantic-content="27,29" data-semantic-parent="32"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="27" data-semantic-parent="30" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="28" data-semantic-parent="30">λ <!-- λ --> </mi> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="29" data-semantic-parent="30" data-semantic-operator="fenced">)</mo> </mrow> </msubsup> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="57" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="36" data-semantic-children="34" data-semantic-content="33,35" data-semantic-parent="58"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="33" data-semantic-parent="36" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="34" data-semantic-parent="36">x</mi> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="35" data-semantic-parent="36" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="37" data-semantic-parent="59" data-semantic-operator="fenced">|</mo> </mrow> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="inequality" data-semantic-id="38" data-semantic-parent="63" data-semantic-operator="relseq,&lt;">&lt;</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="52" data-semantic-children="44,51" data-semantic-parent="63"> <msup data-semantic-type="superscript" data-semantic-role="integer" data-semantic-id="44" data-semantic-children="39,43" data-semantic-parent="52"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="39" data-semantic-parent="44">2</mn> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="43" data-semantic-children="40,42" data-semantic-content="41" data-semantic-parent="44"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="40" data-semantic-parent="43">1</mn> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="41" data-semantic-parent="43" data-semantic-operator="infixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="42" data-semantic-parent="43">λ <!-- λ --> </mi> </mrow> </msup> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="51" data-semantic-children="45,49" data-semantic-content="50,45" data-semantic-parent="52"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-id="45" data-semantic-parent="51" data-semantic-operator="appl">Γ <!-- Γ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="50" data-semantic-parent="51" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="49" data-semantic-children="47" data-semantic-content="46,48" data-semantic-parent="51"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="46" data-semantic-parent="49" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="47" data-semantic-parent="49">λ <!-- λ --> </mi> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="48" data-semantic-parent="49" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <annotation encoding="application/x-tex">{(n+\lambda )^{1-\lambda }(1-x^{2})^{{\frac {1}{2}}\lambda }|C_{n}^{(\lambda )}\left(x\right)|&lt;{\frac {2^{1-\lambda }}{\Gamma \left(\lambda \right)}}}</annotation> </semantics> </math>